Charles Wilson, who was chief executive of Booker Group before its merger with the supermarket giant, was diagnosed after an operation to remove his tonsils in April.
Tesco said he had been undergoing daily radiotherapy in May and June and was responding well to treatment.
However, Mr Wilson will be stepping down from the Tesco board due to the illness and “the need for Charles to remain vigilant in his recuperation”.
Mr Wilson will remain on the Tesco executive committee, and will focus on the Booker business.
Jason Tarry, currently the group’s chief product officer, will become the chief executive of Tesco UK.
Andrew Yaxley, currently chief executive of Tesco in Ireland, will step up to the role of group chief product officer, and will join Tesco’s executive committee.
Mr Wilson has been at the helm of Booker Group since 2005, and has been tipped by analysts to replace Dave Lewis as the head of Tesco group.
The news comes after Tesco announced it will form a “strategic alliance” with French retailer Carrefour as part of efforts to cut prices.
The long-term deal will be covered by a three-year framework and see the two companies form a “strategic relationship” when dealing with global suppliers.
In June, Tesco reported its 10th consecutive quarter of sales growth, boosted by its acquisition of Booker.
Tesco’s UK supermarket sales rose 2.1% on a like-for-like basis, while Booker’s sales, including tobacco, jumped 14.3% over the period.